The present invention relates to an air fuel ratio control apparatus for controlling a fuel injection amount so that the air fuel ratio of an air-fuel mixture to be supplied into an engine becomes a theoretical air fuel ratio, and more particularly to an air fuel ratio control apparatus for controlling the air fuel ratio with a rapid response (high responsibility) irrespective of variation of the EGR rate.
Generally, in accordance with the so-called modern control theory, such an air fuel ratio control apparatus is arranged to construct a dynamic model of a system for controlling the engine air fuel ratio on the basis of an approximation of an auto regressive model having a degree of 1 and having a dead time P (P=0, 1, 2, . . . ) and in consideration of disturbances so as to determine an air fuel ratio control amount on the basis of an state variable and an optimal feedback gain predetermined on the basis of the dynamic model. The optimal feedback gain is determined so that the responsibility is compatible with the stability under various operating conditions, for example, as disclosed in the Japanese Patent Provisional Publication No. 1-110853. Further, for preventing an oxygen (O.sub.2) sensor output from being shifted to a rich side with respect to the actual density due to the ununiformity of the distribution of the exhaust reflux to the respective cylinders of the engine so as not to control the air fuel ratio to the lean side, when performing the exhaust reflux, the integration constant or the skip amount is switched to a value so that the air fuel ratio tends to become at the rich side as disclosed in the Japanese Patent provisional Publication No. 2-55849 (where the air fuel ratio control is based on the PI control). However, there is a problem which arises with such an air fuel ratio control apparatus based on the modern control theory in that the dynamic model of the engine varies in accordance with the EGR rate. More specifically, as shown in FIG. 7, in the case that the combustion gas flows back (ERG-ON), the time constant (the variation of the air fuel ratio A/F relative to the variation of the air fuel ratio correction coefficient FAF) becomes longer as compared with the case that it does not flow back (EGR-OFF), because the variation of the air fuel ratio determined by the injection amount and air newly sucked is averaged with the air fuel ratio of the combustion gas introduced into the intake system. Thus, if performing the air fuel ratio control in areas, different in EGR rate from each other, on the basis of the feedback gain produced in accordance with the same model, there is the possibility that the air fuel ratio control performance deteriorates due to the model error. In addition, in the case that like the above-described conventional apparatus the air fuel ratio is merely controlled to be inclined to the rich side, when effecting the air fuel ratio control in accordance with the modern control, it is impossible to eliminate the deterioration of the air fuel ratio control performance due to the lag of the responsibility caused by the EGR rate variation.